A second order closure model for calculating the turbulence fluxes in atmospheric boundary layer


1 Assistant Professor, Space Physics Department, Institute of Geophysics, University of Tehran, Iran

2 Ph.D. Student, Western Ontario University, Waterloo, Canada

3 Research Assistant, Institute of Geophysics, University of Tehran, Iran


Turbulent fluxes in the atmospheric boundary layer are calculated using different models. One of the most popular and operational models in this groundwork is the second order turbulent model of Mellor and Yamada that has been widely used to simulate the planetary boundary layer (PBL). Despite its popularity, it has been shown that this model has several weeknesses that affect its accuracy. The main deficiency of this model is its inability in distinguishing between vertical and horizontal components of turbulent kinetic energy. Also, this model can not accurately predict the height of the boundary layer. This deficiency in turn can lead to errors in the parameterization of physical processes. Canuto and his colleagues attempt to overcome these deficiencies by introducing a modified model that is an improved version of Mellor and Yamada model. This later model in theory has proven to have more reliable results in computing turbulent fluxes. To verify the results of this theoretical model, the model was coded and verified using some of the available data sets. The data sets used in this study include, the Sodar data of Institute of Geophysics of University of Tehran and Mehrabad airport sounding data. Also the standard Large Edy Simulation data set (LES) introduced in GABLS (Cuxart, 2006) project was examined. For better certainty of the new model performance, the Nakanishi's LES data that used in his study was used and applied to the model. The data used here present a boundary layer of the atmosphere in neutral or Ekman layer condition. Potential temperature does not exist in the Sodar data set and therefore it was computed using measured laps rate in the same data set. The output of model includes the main flux terms, ,, . Results show that the model produces acceptable values for fluxes and have almost the same vertical profile and trend. There are some differences in the predicted values of parameters. It seems that this model could recognize eddies of boundary layer with more accuracy. The differences between the vertical and horizontal TKE distribution is clear. Some of the differences are explained. The results of model as long as the boundary layer conditions match to those that theory proposed or assumed, are reasonable. The analytical data feed to the model results in better output. Compare to a well-known intercomparison program (GABLS project) the results are quite good. The PBL height is defined as the height at which the turbulent kinetic energy or the magnitude of the momentum flux decreases to a small fraction of the corresponding surface value. Results of experiments show that boundary layer height is estimated well in this model. The critical Richardson number predicted by the model is around unity rather than 0.2 as given by previous models. The larger critical Richardson number is in agreement with LES data. Experiments revealed that the presented model is not suitable for boundary layers in which the Richardson numbers within them approach 1 or are larger than 1.